# pdf for the sum of squared iid normal random variables

I am trying to find the distribution/pdf for the sum of squared $X_i$ iid observations from the normal distribution $X_1 ,..., X_n$ ~ $N(\alpha , \alpha)$, i.e. $X_1 ^2 + X_2 ^2 +...+ X_n ^2$.

I was able to find this on Overflow, but I would really appreciate some clarification.